Robust and sparse estimators for linear regression models

Autores
Smucler, Ezequiel; Yohai, Victor Jaime
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust and asymptotic properties of ℓ1-penalized MM-estimators and MM-estimators with an adaptive ℓ1 penalty are studied. For the case of a fixed number of covariates, the asymptotic distribution of the estimators is derived and it is proven that for the case of an adaptive ℓ1 penalty, the resulting estimator can have the oracle property. The advantages of the proposed estimators are demonstrated through an extensive simulation study and the analysis of real data sets. The proofs of the theoretical results are available in the Supplementary material to this article (see Appendix A).
Fil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Yohai, Victor Jaime. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Materia
Lasso
Mm-Estimators
Oracle Property
Robust Regression
Sparse Linear Models
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/66002
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/66002
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Robust and sparse estimators for linear regression modelsSmucler, EzequielYohai, Victor JaimeLassoMm-EstimatorsOracle PropertyRobust RegressionSparse Linear Modelshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust and asymptotic properties of ℓ1-penalized MM-estimators and MM-estimators with an adaptive ℓ1 penalty are studied. For the case of a fixed number of covariates, the asymptotic distribution of the estimators is derived and it is proven that for the case of an adaptive ℓ1 penalty, the resulting estimator can have the oracle property. The advantages of the proposed estimators are demonstrated through an extensive simulation study and the analysis of real data sets. The proofs of the theoretical results are available in the Supplementary material to this article (see Appendix A).Fil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaFil: Yohai, Victor Jaime. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaElsevier Science2017-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/66002Smucler, Ezequiel; Yohai, Victor Jaime; Robust and sparse estimators for linear regression models; Elsevier Science; Computational Statistics and Data Analysis; 111; 7-2017; 116-1300167-9473CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.csda.2017.02.002info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0167947317300221info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:41:29Zoai:ri.conicet.gov.ar:11336/66002instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:41:29.419CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Robust and sparse estimators for linear regression models
title Robust and sparse estimators for linear regression models
spellingShingle Robust and sparse estimators for linear regression models
Smucler, Ezequiel
Lasso
Mm-Estimators
Oracle Property
Robust Regression
Sparse Linear Models
title_short Robust and sparse estimators for linear regression models
title_full Robust and sparse estimators for linear regression models
title_fullStr Robust and sparse estimators for linear regression models
title_full_unstemmed Robust and sparse estimators for linear regression models
title_sort Robust and sparse estimators for linear regression models
dc.creator.none.fl_str_mv Smucler, Ezequiel
Yohai, Victor Jaime
author Smucler, Ezequiel
author_facet Smucler, Ezequiel
Yohai, Victor Jaime
author_role author
author2 Yohai, Victor Jaime
author2_role author
dc.subject.none.fl_str_mv Lasso
Mm-Estimators
Oracle Property
Robust Regression
Sparse Linear Models
topic Lasso
Mm-Estimators
Oracle Property
Robust Regression
Sparse Linear Models
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust and asymptotic properties of ℓ1-penalized MM-estimators and MM-estimators with an adaptive ℓ1 penalty are studied. For the case of a fixed number of covariates, the asymptotic distribution of the estimators is derived and it is proven that for the case of an adaptive ℓ1 penalty, the resulting estimator can have the oracle property. The advantages of the proposed estimators are demonstrated through an extensive simulation study and the analysis of real data sets. The proofs of the theoretical results are available in the Supplementary material to this article (see Appendix A).
Fil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Yohai, Victor Jaime. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
description Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust and asymptotic properties of ℓ1-penalized MM-estimators and MM-estimators with an adaptive ℓ1 penalty are studied. For the case of a fixed number of covariates, the asymptotic distribution of the estimators is derived and it is proven that for the case of an adaptive ℓ1 penalty, the resulting estimator can have the oracle property. The advantages of the proposed estimators are demonstrated through an extensive simulation study and the analysis of real data sets. The proofs of the theoretical results are available in the Supplementary material to this article (see Appendix A).
publishDate 2017
dc.date.none.fl_str_mv 2017-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/66002
Smucler, Ezequiel; Yohai, Victor Jaime; Robust and sparse estimators for linear regression models; Elsevier Science; Computational Statistics and Data Analysis; 111; 7-2017; 116-130
0167-9473
CONICET Digital
CONICET
url http://hdl.handle.net/11336/66002
identifier_str_mv Smucler, Ezequiel; Yohai, Victor Jaime; Robust and sparse estimators for linear regression models; Elsevier Science; Computational Statistics and Data Analysis; 111; 7-2017; 116-130
0167-9473
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.csda.2017.02.002
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0167947317300221
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.069144

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